Final answer:
When making a turn on a bicycle, the rider needs to lean at a specific angle to maintain balance. This is because the force of the ground on the wheel needs to be on a line through the center of gravity. The relationship among the angle of the turn, the speed of the bicyclist, and the radius of curvature of the turn is similar to the ideal banking of roadways.
Step-by-step explanation:
When a bicyclist is making a turn on level ground, they need to lean at a specific angle in order to maintain balance. This is because the force of the ground on the wheel needs to be on a line through the center of gravity. The net external force on the system is the centripetal force, which is the force needed to keep the bicyclist moving in a curved path.
In order for the turn to be properly balanced, the horizontal component of the force on the wheel must equal the centrifugal force. The vertical component of the force on the wheel cancels out the weight of the system. The relationship among the angle of the turn, the speed of the bicyclist, and the radius of curvature of the turn is similar to that of the ideal banking of roadways. This means that the angle of the turn will depend on the speed of the bicyclist and the radius of the curve.